# Question: In the text we noted that when the Xi are all

In the text, we noted that

when the Xi are all nonnegative random variables. Since an integral is a limit of sums, one might expect that

whenever X(t), 0 ≤ t < ∞, are all nonnegative random variables; and this result is indeed true. Use it to give another proof of the result that, for a nonnegative random variable X,

Define, for each nonnegative t, the random variable X(t) by

Now relate

when the Xi are all nonnegative random variables. Since an integral is a limit of sums, one might expect that

whenever X(t), 0 ≤ t < ∞, are all nonnegative random variables; and this result is indeed true. Use it to give another proof of the result that, for a nonnegative random variable X,

Define, for each nonnegative t, the random variable X(t) by

Now relate

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